To begin, its relevant to look at the skip itself. For some reason, board games are being affected by an anomalous source that changes the fundamental dynamics of the game as long as they fulfil certain roles. In addition, the two players are essentially possessed by two childish gods, the Sculptor and the Artist.
These gods have been playing a game between themselves for untold eons. A simple game of simple rules which are the following:
A white sphere with less than two white sphere's neighboring it becomes a black sphere
A white sphere with two or three white spheres surrounding it remains
A white sphere with more than three white sphere's neighboring it becomes a black sphere
A black sphere with exactly three white sphere's neighboring it becomes a white sphere.
The rules of the game mean that the Sculptor wins every single time. This is actually a good thing because although the Sculptor's victory means that death and mortality prevail in the universe, the sphere's representing individual stars throughout the universe, the reverse, that of the Artist winning is much more damning for the world. The Sculptor represents his final shape, the Final Shape of Truth. Everything dies, and only the strong survive.
The Artist believes that life should not be finite and condemned to the heat death of the universe, but rather that it should flourish forever. She dreams of garden worlds, paradises and riches beyond our wildest imaginations that her "children" would cherish forever. The Artist represents the Final Shape of Ideal. Everything lives forever as paracausal beings that do not fear death and the "meek shall inherit". In truth, however, the Artist's garden worlds would die, they would be burnt by reality benders and the people of every planet would be enslaved because immortal god-like beings are really total assholes.
The Artist has created this anomalous effect to break herself free of her constant loses at the game. She is trying to systematically find a player so good at the game that they can defeat the Sculptor and project her version of reality into the world. This is explored through audiovisual recordings of the Artist and Sculptor playing their game together.
And the kicker is that at first, the Foundation simply stored the board games away within Site-21, at first, it only affected chessboards but then it spread to checkerboards, packs of cards, battleships, any game was rife for the anomalous effect to occur. And then the Foundation began burning any instances of SCP-XXXX-1 after they realise what is really happening. An additional log explains that they can't just stop people making board games as them containing the first instance led to it spreading to other board games. What if it spreads to picking flowers? What if it spreads to something entirely random that they can't stop, like flipping coins or cutting down plants? So their only chance of stopping this phenomenon is to contain every single board game that comes under the effect but eventually, the Artist may get her wish.